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## Cost-Volume-Profit Analysis

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**Cost-Volume-Profit Analysis**Chapter 7**Cost Volume Profit Analysis**• What Is the Break-Even Point? • What Is the Profit at Occupancy Percentages Above Break-Even? • How Do Increases in Fixed Charges Affect Break-Even? • How Many More Rooms Must Be Sold to Recover Cost Increases?**Cost Volume Profit Analysis**• How Many Rooms Must Be Sold to Reach a Certain Profit? • What Is the Effect of Profits When Prices, Variable Costs, and Fixed Costs Change? • How Do Labor Rate Changes Affect Profits?**Cost-Volume Profit Assumptions**• Fixed Costs Remain Constant During the Period Being Analyzed. • Variable Costs Fluctuate in a Linear Fashion With Revenues. • Variable Costs Are Constant on a Per Unit Basis.**Cost-Volume Profit Assumptions**• Productivity Remains Constant. • Revenues Are Proportional to Variable Costs. • There Are No Volume Discounts.**Cost-Volume Profit Assumptions**• All Costs Can Be Broken Down Into Their Fixed and Variable Components. • Joint Costs Are Not Eliminated When One Department Is.**CVP Basic Formula**• How Much Should Be Charged to Break-Even? • 10 Room Motel • Variable Costs Are $5 Per Room • Fixed Costs Are $2,500**CVP Basic Formula**• 250 Rooms Will Be Sold • SP = VC Per Room + (Fixed Costs / Number Rooms Sold) • SP = $5 +( $2,500 / 250) • SP = $15 Per Room**Most Common Expression of CVP Analysis Is a Graph**Loss but cover FC Profit Breakeven Loss**CVP Basic Formula**• How Much Should Be Charged to Earn $2,000 in a 30 Day Period? • 10 Room Motel • Variable Costs Are $5 Per Room • Fixed Costs Are $2,500**CVP Basic Formula**• 250 Rooms Will Be Sold • SP = VC Per Room + (Profit + FC) / Number Rooms Sold • SP = $5 +( $2,000 + $2,500) / 250 • SP = $23 Per Room**CVP Formula for Single Product Analysis**• I = Net Income • S = Selling Price • X = Units Sold • V = Variable Costs Per Unit • F = Total Fixed Costs (Plus Profit)**CVP Formula for Single Product Analysis**• SX = Total Revenue • VX = Total Variable Costs • Basic Formula for Break-Even (Income Equals 0) • 0 = SX - VX - F**Break-Even Formula Variations**• Units Sold at Break-Even • X = F / (S - V) • Fixed Costs at Break-Even • F = SX - VX • Selling Price at Break-Even • S = (F / X) + V**Break-Even Formula Variations**• Variable Cost Per Unit at Break-Even V = S - (F / X) • Most Hospitality Operations Sell Multiple Products. Therefore, We Need Additional Tools.**Contribution Margin**• Contribution Margin (CM) Is the Selling Price, or Sales, Minus the Variable Cost(s). • Contribution Margin Percentage (Ratio) Is the CM Divided by the Selling Price (or Sales).**Contribution Margin**• To Get Break-Even in Units, Divide the Fixed Costs by the Contribution Margin. • To Get Break-Even in Sales Dollars, Divide the Fixed Costs by the Contribution Margin Percentage.**Contribution Margin**• Since Our Products Have Different CM, We Use CM Percent (Weighted) a Lot.**Weighted Contribution Margin Percent**• The Contribution Margin Percent, or Contribution Margin Ratio (CMR) Says That the Amount Available to Cover Fixed Costs Is the CMR Times the Sales Dollars.**Weighted Contribution Margin Percent**• The Weighted CMR Is Computed As Follows: • (Total Revenue - Total Variable Costs) / Total Revenue**Weighted Contribution Margin Percent**• Another Way of Looking at it is to Take the Sales Mix Percentage for Each Area (Which in Total Must Add up to 100%) and Multiply That Percentage by the CMR for the Particular Area. Then Add All Results to Get the Weighted CMR.**Weighted Contribution Margin Percent**• Divide the Weighted CMR Into the Fixed Costs (and Profit if Applicable) and the Result is the Required Sales Level.**Margin of Safety**• Excess of Budgeted or Actual Sales Over Sales at Break-Even • Expressed in Units or Dollars**Sensitivity Analysis**• Study of the Sensitivity of Dependent Variables to Changes in Independent Variables • Looks at the Incremental Number of Units Required to Sold to Cover Additional Costs**Operating Leverage**• Extent to Which Expenses Are Fixed Rather Than Variable • Highly Levered When Fixed Costs to Variable Costs Is High • Highly Levered Means a Small Increase in Sales Yields a Large Profit (Above Break-Even)**Providing for Income Taxes**• In Most Situations We Will Know What the After Tax Income is Needed to be and the Tax Rate. The Problem is to Compute the Before Tax Income (So That it Can be Added to Fixed Costs).**Providing for Income Taxes**• Tax = T • Tax Rate = R • After Tax Income = A • Before Tax Income = B**Providing for Income Taxes**• B * R = T and B - T = A • Substitute (B * R) for T and We Have: • B - (B * R) = A or B * (1 - R) = A or • B = A / (1 - R)